Somebody Please solve this question without using L Hospital rule.
Evaluate if:
Answers
Answer:
1/2
Step-by-step explanation:
Given that,
[tex]\lim_{n \to 1} (\dfrac{1+\cos\pi x}{\tan^2\pi x})[/tex]
Using L Hospital's rule to find it :
[tex]\lim_{n \to a} \dfrac{f(x)}{g(x)}= \lim_{n \to a} \dfrac{f'(x)}{g'(x)}[/tex]
We have,
a = 1, [tex]f(x)=1+\cos\pi x, \ \ g(x)=\tan^2\pi x[/tex]
[tex]f'(x)=\dfrac{d}{dx}(1+\cos\pi x)\\\\=-\pi \sin \pi x\ .....(1)[/tex]
[tex]g'(x)=\dfrac{d}{dx}(\tan^2\pi x)\\\\=2\tan\pi x\times \sec^2\pi x\times \pi\ .....(2)[/tex]
From equation (1) and (2) :
[tex]\lim_{n \to 1} \dfrac{f(x)}{g(x)}= \lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\\lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\=\lim_{n \to 1} \dfrac{-1}{2}\times\cos^3\pi x\\\\=\dfrac{-1}{2}\times \cos^3\pi \\\\=\dfrac{1}{2}[/tex]
So, the value of the given function is 1/2.
Related Questions
7th grade math
Find the value of the expression. mp = 6 for m 6 and p = 3
Answers
step by step:
please help me
find the slope and explain what the slope represents
write the equation of the line
what does the y-intercept represent
using the equation calculated the length of the spring when 15 ib. of the weight is attached
Answers
Answer:
Slope=2
y intercept= Length of spring without any weight
15 lbs= 38 inches
Step-by-step explanation:
slope=
18-12/5-2= 6/3 = 2
y intercept= 0=x and x=amount of weight
equation= 2x+8=y
2(15)+8=38
1
1
Consider the polynomial function:
p(x) = 3x3 + 10x2 + ax - 6
where a is an unknown real number.
If
(x + 3)
is a factor of this polynomial what is the value of a? Show all the steps below.
Answers
Step-by-step explanation:
By Factor Theorem, p(-3) = 0.
Therefore 3(-3)³ + 10(-3)² + (-3)a - 6 = 0 and a = 1.
Is (x+1)/x^2 greater or less or equal to 1/x
Answers
Answer:
(1) x^2 is greater than 1.
(2) x is greater than -1.
(1) x^2 is greater than 1 --> x2>1x2>1 --> x<−1x<−1 or x>1x>1. Sufficient.
(2) x is greater than -1 --> x>−1x>−1. Not sufficient.
Find the real numbers x and y that make the equation true. (2 points)
-3 + yi = x + 6i
Answers
Answer:
x = - 3, y = 6
Step-by-step explanation:
For the 2 sides to be equal then the coefficients of the imaginary terms and the real terms must be equal.
Given
- 3 + yi = x + 6i , then
x = - 3 and y = 6
Given: \overline{BD} \cong \overline{BE}, BD ≅ BE , \overline{DE} DE bisects \overline{AB} AB and \overline{DE} DE bisects \overline{BC}. BC . Prove: \overline{AB} \cong \overline{BC} AB ≅ BC .
Answers
Given:
[tex]\overline{BD} \cong \overline{BE}[/tex]
DE bisects [tex]\overline{AB}[/tex].
DE bisects [tex]\overline{BC}[/tex].
To prove:
[tex]\overline{AB} \cong \overline{BC}[/tex]
Proof:
DE bisects [tex]\overline{AB}[/tex]
Then, [tex]AD=BD[/tex]. ...(i)
DE bisects [tex]\overline{BC}[/tex].
Then, [tex]BE=CE[/tex]. ...(ii)
We have,
[tex]\overline{BD} \cong \overline{BE}[/tex] ...(iii)
Using (i), (ii) and (iii), we get
[tex]\overline{AD} \cong \overline{CE}[/tex] ...(iv)
Adding (iii) and (iv), we get
[tex]\overline{BD}+\overline{AD} \cong \overline{BE}+\overline{CE}[/tex]
[tex]\overline{AB} \cong \overline{BC}[/tex]
Hence proved.
PLEASE HELP ME!! An eagle eats 6 pounds of food every 8 days.How long does it take the eagle to eat 90 pounds of food
Answers
Answer:
15 days
Step-by-step explanation:
8 days equals 48 pounds of foods. 48 times 2 will be 96 and that equals 16 days. Subtract 6 from 96 and you get 90 but you have to subtract a day as well.
Answer:
120 days
Step-by-step explanation:
6/8 = 0.75 meaning the eagle eats 0.75 pounds of food every day.
90/0.75=120 days
ILL GIVE BRAINLIEST ON THIS QUESTION!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
15.25 or 15 if you need it to be rounded.
Step-by-step explanation:
-11 on both sides to get 5x=1x+61. Then, -1x on both sides to get 4x=61. Then to find x you do 61 divided by 4 which is 15.25.
is the surface area of the octahedron?
10.4 cm
12 cm
12 cm
12 cm
X
+
Answers
the answer is 576 2 cm
Step-by-step explanation:
hope i helped
PLEASE HELP!!!! DUE RIGHT NOW!!!! WILL GIVE BRAINLIEST!!!!!
What is the equation, in standard form, of a parabola that models the values in the table?
Answers
y=4x^2+5x-6y=4x2+5x−6
:
Given points are :
x = -2 0 4
y=f(x) = 0 -6 78
We have to model the parabola with the help of these points
Solution:
We consider a standard equation of parabola y= ax^2+bx+cy=ax2+bx+c
now, we put the points in the equation we get,
at (-2,0) is 4a-2b+c=0
at (0,-6) is c=-6
at (4,78) is 78= 16a+4b+c
now, solving these equation we get, a= 4 , b= 5 , c= -6
so the equation formed with these points is y=4x^2+5x-6y=4x2+5x−6
we can see this in the graph attached.
Step-by-step explanation:
Hope this helps!! :D
Answer:
the answer to 14 is D
and 15 is i think x= [tex]\frac{5+\sqrt{13} }{2}, \frac{5-\sqrt{13} }{2} \\[/tex]
Step-by-step explanation:
Jim is saving money to buy a game. So far he saved $36, which is three-fourths of the total cost of the game. How much does the game cost?
Answers
Answer:
$48
Step-by-step explanation:
Because he has 3/4 you would divide 36 by 3 whick is 12 then multiply by 4 to get the total of $48
Answer:
$48 :)
Step-by-step explanation:
In a class there are 12 girls and 18 boys. What is the ratio of girls to students in simplest form?
Answers
Answer:
Step-by-step explanation:
12:18
can both be divided by 6
answer is 2:3
Answer:
6:9
Step-by-step explanation:
that's the simplest form
15t +95 + 5 - 9
i need help asap
Answers
I need to k ow the answer pls show work
Answers
Say 5 of your favorite things and whoever has the most of my favorite stuff gets brainlest
Answers
Answer:
food, video games, sports, naps, music
Step-by-step explanation:
In 1 hour the employee dropped 635 chocolates. If this represents 25% of the days chocolate molds, how many chocolates were planned to be
produced
Answers
Answer:
2540
Step-by-step explanation:
25% is a quarter of 100% so if 635 is 25% you multiple 635 x 4 to get your final answer concluding in 2540. if i'm wrong let someone else correct me :b
TWO MULTIPLE CHOICE QUESTIONS PLS HELP
Answers
Answer:
sorry i only know the number 2.
so the answer is the first one...
2/3 + 1/3 x 3/4 in simplest form
Answers
Answer:
11/12
Decimal form: 0.916 (the 6 is continuous)
Step-by-step explanation:
Do you guys know this one if so comment the down the answers that all apply in the can't tysm!
Answers
Answer:
7 to the fourth power, 7*7*7*7 , and 7^4
Step-by-step explanation:
Answer:
7 x 7 x 7 x 7
7 to the fourth power
7^4
Step-by-step explanation:
Please i need help jk im lazy ZZZzzzzzz
Answers
Answer:
the first one is $6.66
Step-by-step explanation:
the 3 items added up is 74 cents, then 74 is multiplyed by 9.
Find the measure of each exterior angle of the regular polygon.
Answers
Answer:
30°Step-by-step explanation:
Sum of exterior angles of the regular polygon is 360°The pictured is 12-gon
Each exterior angle measures:
360°/12 = 30°Answer:
30 degrees
Step-by-step explanation:
(Sum=360)
360/12=30
(We got 12 because there are 12 sides in the polygon!)
Angela transfers 15% of each paycheck she received into her savings account. If she transferred $54 into her savings account last week, how much did she earn on that paycheck? Show your work using a model, proportion or equation
Answers
Answer:
$360
Step-by-step explanation:
Let the amount that she earned on the paycheck be represented by x
Hence,
15% of x = $54
Therefore:
15/100 × x = $54
15x/100 = $54
Cross Multiply
15x = $54 × 100
15x = $5400
x = $5400/15
x = $360
Therefore, the amount that she earned on that paycheck = $360
Write an inequality to fit the given inequality the line pass through (0,1) and (1,3)
Answers
Answer: Y< 2/1x +1
Step-by-step explanation: (Slash mark means a fraction)
You are at a trade show where you are selling baseball cards for $4 a car and buyng baseball cards for $6 a card. If you started the day with $200, how much money do you have at the end of the day if you sold c baseball cards and bought b baseball cards?
Answers
Answer:
He can sell 80 baseball card and buy 120 cards
Step-by-step explanation:
if thats good
Two friends shop for fresh fruit Elena buy a watermelon for 8.55 and 3 pounds of cherries. Taniy buys a pineapple for 2.45 and 2 pounds cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to how much more Elena spent.
Answers
Answer:
$6.10 + p
Step-by-step explanation:
Given that:
p = price in $ per pound of cherries
ELENA:
Amount spent = 8.55 + 3p
TANIY:
Amount spent = 2.45 + 2p
How much more Elena spent :
Amount spent by Elena - Amount spent by Taniy
(8.55 + 3p) - (2.45 + 2p)
8.55 + 3p - 2.45 - 2p
8.55 - 2.45 + 3p - 2p
6.10 + p
$6.10 + p
What is the slope for y=-7x+12
Answers
Answer:
-7
Step-by-step explanation:
Answer:
-7. the number with x is always the slope in this sort of equation. The 12 in this equation is the y-intercept
Step-by-step explanation:
make m the subject of g-3m=am+5
Answers
Answer:
m = (g - 5) / (a + 3)
Step-by-step explanation:
g-3m=am+5
Get all the m's on one side.g - 5 = am + 3m
Combine the m's into one term, using bracketsg - 5 = (a + 3)m
Get m on it's own by dividing by a + 3(g - 5) / (a + 3) = m
Answer:
[tex]\displaystyle m=\frac{g-5}{3+a}[/tex]
Step-by-step explanation:
Equation Solving
To solve an equation for a specific variable, we perform a sequence of steps to have that variable isolated or make it the subject of the equation.
We are given the expression:
[tex]g - 3m=am+5[/tex]
And it's required to make m the subject of the equation. This means we have to isolate m at the left side of the equation.
First, multiply both sides by -1;
[tex]-g + 3m=-am-5[/tex]
Add am:
[tex]-g + 3m+am=-5[/tex]
Add g:
[tex]3m+am=-5+g[/tex]
The variable m is found in both term, thus we factor it out:
[tex]m(3+a)=g-5[/tex]
Dividing by 3+a:
[tex]\mathbm{\displaystyle m=\frac{g-5}{3+a}}[/tex]
BRAINLIEST LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A: X-55>25
B: X-25>55
C:X+55>25
D:X+25>55
Answers
Answer:
B
Step-by-step explanation:
Answer:
First one would be B
Second one would be x ≥ 80
The first humor bookshelf in the section of a library can hold 2296, books. The bookshelf has 7 shelves. Shelves. Each shelf can hold the same number of books. How many books can each shelf hold? Write an equation to help solve this problem.
Answers
Answer:
328 books
An equation to solve the problem:
7x = 2296
Step-by-step explanation:
The first humor bookshelf in the section of a library can hold 2296, books. The bookshelf has 7 shelves. Shelves. Each shelf can hold the same number of books. How many books can each shelf hold? Write an equation to help solve this problem.
They said each shelf can hold the same number of books
And we have 7 shelves
Total number of books = 2296
Hence:
The number of books each shelf can hold = 2296 books/7 Shelves
= 328 books
Hence, each shelf can hold 328 books
An equation to solve this problem =
Number of books can be represented by x
Hence:
7x = 2296
what is the value of p
Answers
Answer:
p = 61 degrees
Step-by-step explanation:
The sum of all angles that make up a striaght line is 180 degrees. To find p you just subtract the other angles from 180: 180 - 87 - 32 = 61.
